As part of our attack on the protein-folding problem, we have been applying simple statistical-mechanical models to the study of secondary-structure formation in proteins. The formation of both beta-hairpin and alpha-helical structures has been studied using the same simple physical picture: The backbone structure of polypeptide chains is described in terms of the conformations of individual structural units, which are pairs of flexible backbone dihedral angles. These units are viewed as having only two possible conformational states, the "native" state, corresponding to the conformation assumed by the unit in the native structure of the chain, and the "random-coil" state, which encompasses all non-native conformations. The structural states of a polypeptide chain are then identified by the sequence of native/random-coil states of these dihedral-angle pairs. In recent years we have successfully used this simple picture to model the equilibrium and kinetic properties of small secondary-structure-forming peptides; we are currently adapting this approach to model the folding properties of the complete polypeptide chains of protein molecules. As before, the structural states of a chain are characterized by the specific sequence of native/random-coil dihedral-angle pairs. The stability of any such state is determined by the offsetting effects of entropy loss associated with fixing dihedral-angle pairs in the native conformation, and native non-bonding contacts between different parts of the chain separated by sufficiently long contiguous stretches of native dihedral-angle pairs. For a given chain these stabilizing contacts are identified by analyzing available X-ray crystallographic or NMR-derived structures of the corresponding protein. Specified values for the entropy loss of fixing a single unit in the native conformation and for the overall strength of the intra-chain contacts are then used to compute a model partition function of the chain. Because of the intractably large number of states that arise from complete enumeration of the possible combinations of dihedral-angle-pair states in even a moderately long chain, we compute the partition function mainly using the "single-sequence" and "double-sequence" approximations--i.e., only considering states which have at most one and two contiguous stretches of native dihedral-angle pairs, respectively. These simplified partition functions are used to compute the free energy for a given chain as a function of a single reaction coordinate given by the total number of native dihedral-angle pairs; this "reaction free-energy surface" provides the basis for modeling the equilibrium and kinetic folding properties of the chain. We have found that this approach gives a useful qualitative picture of folding in simple proteins, and we are currently assessing the utility of this type of statistical-mechanical model for describing the folding of more complicated proteins and the effects of mutations on folding properties.